LAUSR

Abstract The 2D contrast source inversion (CSI) method is introduced for interpreting cross-hole radio imaging (RIM) data. The contrast source is defined as the product of the electric field and the object profile, the latter of which contains information about the conductivity and the permittivity of a model. We built a cost function and used the conjugate gradient iterative method to minimize the cost function by alternatively updating the contrast source and the object profile. We proposed an equivalent 2D model as the background model, one of the input parameters in the inversion. To demonstrate the effectiveness of CSI, we applied the method to synthetic data generated from 3D models calculated with a finite element modelling package (Comsol Multiphysics). Specifically, we inverted a) data from a prismatic perfect conductor model, b) the same data with noise, c) the same data, but with transmitters only in a single borehole, and d) the data from a model with an L-shaped perfect conductor. We conclude that isolated conductors between the holes can be identified with the inverted conductivity model. For the conductors larger than half the wavelength, the location and shape can be interpreted with confidence; for smaller conductors, the central location can be interpreted from the inverted conductivity. The modelling studies with the noisy data show that the CSI method is very robust to the existence of noise. The experiment with the transmitter location only in single borehole shows that the single borehole data are not enough to provide satisfactory inversion results. From the synthetic studies, we infer that the conductivity values cannot be correctly estimated from the inversion results. The inversion times for the data in this paper are less than 20 min for 200 iterations, which is reasonable and significantly less than the computation time for the 3D synthetic data.